[Captain Beeflat]

patmiller has pretty well covered it.
The C tenor is a bit of a chameleon & can sound tenor-like, alto-like, or, heaven forfend. it can sound like a C melody. This latter sound is the reason why it did not survive...thin, stuffy, weedy, quiet & farty.
As pat says, the Martin certainly has the beefiest sound, so, with a tenor mouthpiece, it can sound remarkably tenor-like.
So, you choice of mouthpiece really depends upon your intended use of the horn.
If you have no friends, little musical taste, & live with your parents, then I heartily recommend the original C tenor mouthpiece.
If you play in a Folkie Band or in church, I would recommend the oh-so-sweet, well engineered Conn with either an alto or modern C tenor piece.
For Down & Dirty Blues or R&R, (ie. PROPER saxophone) one instinctively reaches for the Martin with the weapons grade tenor mouthpiece.
Welcome to the sax pariahs' club.

 

[Captain Beeflat]

Welcome Marc Daniel! Lots of good advice from the CMel. players here. Wish I had a Martin!

sandy.
If you thought that the Conn sounded like a tenor you really should buy a Martin.
If you play in a tenor style it is the horn for you....with, of course, a tenor mouthpiece
I am a recent convert.....now I use my Martin Typewriter C tenor exclusively, the difference in cojones is remarkable.
Sadly my TT & L&H are relegated, in their cases, under the bed.

 

[Captain Beeflat]

I was suggesting an artificial reed such as the fibracell but maybe this is a tad too complicated to find especially if you are not sure which strength of reed you can handle.

Also too expensive at this stage. The synthetics all have their particular nuances...it would be a costly procedure to try them all in different strengths, to find the reed that suits you.
However, in my experience, once you have found the right strength of the right synthetic your reed problems are over....I hasten to add that this is only my experience.
For the time being I would follow milandros advice.